Shouldn't the error on a quad double be way smaller than this? I'm not sure what specific numbers you're operating on, but if your answers are on the order of 10^0, then shouldn't you have around 63 decimal digits of accuracy, rather than just 4 more orders of magnitude? Wouldn't an error of 1e-17 be like using mpfr with ~60+ bits?
I guess what I'd like to see to understand this better is the absolute magnitude of cos(1) between rdf, qr, mpfr(212), and mpfr(1000). On Feb 26, 2007, at 7:07 PM, didier deshommes wrote: > How accurate are these results? The error is quite small and more > accurate than computing with ieee doubles (most of the time, about 4 > orders of magnitude). Here: > -- "mpfr vs qd " is the absolute error between a quad double and mpfr > real, and > -- "mpfr vs rd" is the absolute error in between a real double and > mpfr real: > > cos: > mpfr vs qd: 5.4180459105735642433E-17 > mpfr vs rd: 3.57935903139e-13 > > sin: > mpfr vs qd : 4.9262450620608075647E-17 > mpfr vs rd :4.22384349719e-13 > > tan: > mpfr vs qd : 1.0996009735470526760E-16 > mpfr vs rd : 1.37401201528e-12 > > acos: > mpfr vs qd : 1.0587913940429450042E-16 > mpfr vs rd : 1.95518601309e-12 > > asin: > mpfr vs qd : 8.8793698896573320837E-17 > mpfr vs rd : 1.95532479097e-12 > > atan: > mpfr vs qd : 4.2348407244178416828E-17 > mpfr vs rd : 4.09228206877e-13 > > cosh: > mpfr vs qd : 1.1001972366209892607E-16 > mpfr vs rd : 4.91606755304e-13 > > sinh: > mpfr vs qd : 7.7307263905133232438E-17 > mpfr vs rd : 6.54809539924e-13 > > tanh: > mpfr vs qd : 5.0901691104837936913E-17 > mpfr vs rd : 4.08617584213e-13 > > cosh: > mpfr vs qd NAN > mpfr vs rd nan > > sinh: > mpfr vs qd : 5.0731042379144584142E-17 > mpfr vs rd : 4.23105994685e-13 > > tanh: > mpfr vs qd : 1.9007614867237325552E-16 > mpfr vs rd : 8.84181616811e-12 > ###################### > > In conclusion: > In most cases it is faster to compute with quad double reals instead > of using mpfr reals at 212 bits. In all cases quad doubles are more > accurate than simple ieee doubles. > > didier > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
